\(\dfrac{x}{12}=\dfrac{x+15}{16}\)

\(16x=12\left(x+15\right)\)

\(16x=12x+180\)

\(4x=180\)

\(x=45\)

B

6C

7C

8C

9A

10D

11C

D

\(n_{Zn}=0,1\left(mol\right)\)

\(m_{HCl}=\dfrac{200.7,3}{100}=14,6\left(g\right)\)

\(n_{HCl}=0,4\left(mol\right)\)

        \(Zn+2HCl\rightarrow ZnCl_2+H_2\)

BĐ : 0,1      0,4

PƯ: 0,1      0,2            0,1       0,1 

SPƯ: 0        0,2           0,1        0,1

\(m_{ZnCl_2}=13,6\left(g\right)\)

\(5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}\)

\(=5\sqrt{3}+5\sqrt{48-10\sqrt{\left(\sqrt{3}+2\right)^2}}\)

\(=5\sqrt{3}+5\sqrt{48-10\left(\sqrt{3}+2\right)}\)

\(=5\sqrt{3}+5\sqrt{48-10\sqrt{3}-20}\)

\(=5\sqrt{3}+5\sqrt{28-10\sqrt{3}}\)

\(=5\sqrt{3}+5\sqrt{\left(5-\sqrt{3}\right)^2}\)

\(=5\sqrt{3}+5\left(5-\sqrt{3}\right)\)

\(=5\sqrt{3}+25-5\sqrt{3}\)

= 25

\(x+x^2-x^3-x^4=x\left(x+1\right)-x^3\left(x+1\right)\)

\(=\left(x-x^3\right)\left(x+1\right)\)

\(=x\left(1-x^2\right)\left(x+1\right)\)

a) \(x=4\rightarrow\sqrt{x}=2\) (TMĐK)

Thay \(\sqrt{x}=2\) vào A ta có :

\(A=\left(\dfrac{1}{2-1}-\dfrac{1}{2+1}\right)=\left(1-\dfrac{1}{3}\right)=\dfrac{2}{3}\)

b) M=A.B

\(\rightarrow M=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+1}\right).\left(\dfrac{x+1}{2}-\sqrt{x}\right)\)

\(\rightarrow M=\left(\dfrac{\sqrt{x}+1-\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right).\left(\dfrac{x+1-2\sqrt{x}}{2\sqrt{x}}\right)\)

\(\rightarrow M=\dfrac{2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}.\dfrac{\left(\sqrt{x}-1\right)^2}{2\sqrt{x}}\)

\(\rightarrow M=\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(M=\dfrac{\sqrt{x}}{6}\)

\(\rightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}}{6}\)

\(\rightarrow6\left(\sqrt{x}-1\right)=\sqrt{x}+1\)

\(\rightarrow6\sqrt{x}-6-\sqrt{x}-1=0\)

\(\rightarrow5\sqrt{x}-7=0\)

\(\rightarrow\sqrt{x}=\dfrac{7}{5}\)

\(\rightarrow x=\pm\dfrac{5\sqrt{7}}{5}\)

\(\rightarrow x=\dfrac{5\sqrt{7}}{7}\) (TMĐK)

a) \(M=\dfrac{x}{x-2}:\left(\dfrac{2x}{x^2-2x}-\dfrac{3}{x}\right)\)

\(M=\dfrac{x}{x-2}:\left(\dfrac{2x}{x\left(x-2\right)}-\dfrac{3\left(x-2\right)}{x\left(x-2\right)}\right)\)

\(M=\dfrac{x}{x-2}:\left(\dfrac{2x-3x+6}{x\left(x-2\right)}\right)\)

\(M=\dfrac{x}{x-2}.\dfrac{x\left(x-2\right)}{6-x}\)

\(M=\dfrac{x^2}{6-x}\)

b) \(x^2-3x=0\)

\(x\left(x-3\right)=0\)

x=0 (KTMĐK) hoặc x=3 (TMĐK)

Thay x=3 vào M ta có :

\(M=\dfrac{3^2}{6-3}=\dfrac{9}{3}=3\)

c) \(M\ge0\rightarrow\dfrac{x^2}{6-x}\ge0\)

\(x^2\ge0\rightarrow6-x\ge0\)

\(x\le6\)

Kết hợp với ĐK, ta có : \(x\le6,x\ne0,x\ne2\)

\(\sqrt{16}+1=4+1=5\)

\(\sqrt{3}.\sqrt{12}=\sqrt{3.12}=\sqrt{36}=6\)